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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_185.52', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.766044443118978, -0.6427876096865394], 'a3': [0.6427876096865394, 0.766044443118978], 'a4': [0.17364817766693036, 0.984807753012208], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [2.9010907910729803e-30, -1.0], 'a7': [0.3420201433256687, -0.9396926207859084], 'a8': [0.5, -0.8660254037844386], 'a9': [-0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 0.8591363881150113, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [37, [1]]], 'bad_primes': [5, 37], 'central_character': '185.52', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 185, 'conductor_radical': 185, 'conjugate': 'dirichlet_L_185.153', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^22', 'a^5', 'a^8', 0, 'a^27', 'a^29', 'a^30', 'a^10', 0, 'a^30', 'a^13', 'a^26', 'a^15', 0, 'a^16', 'a^28', 'a^32', 'a^5', 0, 'a^34', 'a^16', 'a^6', 'a^35', 0, 'a^12', 'a^15', 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'186.21666237331233761935841218245', '186.99046968478416105161334747948', '187.7437499929762853087072160295', '188.50282720947102654665629941284', '189.27553468843137435403899012794', '189.84325051585654063646245605663', '191.08731790139575703684187089626', '191.490837662815747923806870091594', '191.79866096296823814978007475173', '192.60382893815221798533262162712', '193.55069780661593094483022285077', '193.83964053207321497382640206601', '194.74040919329649625236087470049', '195.58695182128957874357541898750', '196.87912883342944906190312942047', '197.433112456396963837448301919475', '197.9461030883982482105384493194', '198.62284297970106362651641465150', '199.26564014804396675216724781291'], 'prelabel': '1-185-185.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8591363881150113, 'root_angle': -0.07214010067318209, 'root_number': '0.899020119538345064701858176098-0.437907324288210267938410820886*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0721401006732', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.951187500013288981322845818097-0.137961651416860665087218188222*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.2044053058', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.99688392417', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.70910989021', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.8591363881150113, 'bad_primes': [5, 37], 'central_character': '185.52', 'conductor': 185, 'conductor_radical': 185, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/185/52'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-185-185.52-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-185-185.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8591363881150113, 'root_angle': -0.07214010067318209, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.2044053058', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_185.52', 'Lhash_array': ['dirichlet_L_185.52'], 'factors': ['1-185-185.52-r0-0-0'], 'label': '1-185-185.52-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/185/52'}
Lfunction data - 1-185-185.52-r0-0-0